Complex Refractive Index Determination Via Microspectroscopy Through Magnifying Optics: Challenges and Opportunities

For the design and optimization of optoelectronic devices, accurate knowledge of the complex refractive indices of the constituent materials is essential. Herein, we present a fast and nondestructive approach for the extraction of the refractive indices from reflectance and transmittance spectra of samples with lateral dimensions down to the micrometer scale. Microspectroscopy, combining an optical microscope and a spectrometer, enables the assessment of the optical response of multilayer stacks using high-magnification optics with correspondingly large numerical apertures. Employing a numerical formalism explicitly accounting for the influence of the numerical aperture allows for wavelength-by-wavelength retrieval of the refractive index with subsequent refinement by dispersion modeling. We demonstrate the applicability of the proposed method for large-area, homogeneous, optically incoherent samples such as transparent glasses and absorbing 4H-SiC, for a ${\mathrm{Si}}_x{N}_y$ thin film on a glass substrate, and for mechanically exfoliated flakes of highly oriented pyrolytic graphite and $\mathrm{Mo}{O}_3$ , as representatives of uniaxial and biaxial optical anisotropy. The proposed approach provides a cost-effective proof of concept for retrieving optical constants of microscale samples under arbitrary numerical apertures. The case of graphite highlights the limitation for discerning the out-of-plane optical constants due to reduced sensitivity. Finally, we discuss paths to probe out-of-plane anisotropy.